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Showing posts from February, 2020

### Cracked The Code!

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**What was the challenge?**

Let's take a look at the given hints once again.

Let's name above numbers as NUMBER 1, NUMBER 2.....NUMBER 5 and hints as HINT 1, HINT 2......HINT 5.

NUMBER 1 and NUMBER 5 has one number common and that is 4 placed at same positions in both. The number 4 can't be the correct number as HINT 1 says it's correctly placed while Hint 5 suggests it is wrongly placed whereas in both numbers it's at same middle position.

So

**4**can't be that CORRECT number.

Numbers

**5,**

**3**and

**0**are eliminated by HINT 2.

So numbers 5 and 4 are thrown out of race in NUMBER 1. Hence, the correct number pointed by HINT 1 must be 8 with it's correct position. Now, we got 1 digit of unlocking code XX8.

Now 5 also eliminated from NUMBER 3 leaving behind

**1**and

**7**as correct numbers pointed by HINT 3 but in wrong positions.

Since position of 1 is wrong and third digit of the code being already occupied correctly by 8 the 1 must be at second place of the code. And hence 7 must b…

### "Go The Distance"

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There are

**50 bikes**with a tank that has the capacity to go**100 km**. Using these 50 bikes, what is the**maximum**distance that you can go?**Here is the maximum distance calculation!**### Maximizing The Distance!

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**What was the challenge?**

Remember, there are 50 bikes, each with a tank that has the capacity to go 100 kms.

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**SOLUTION 1 :**

Any body can think that these 50 bikes together can travel 50 x 100 =

**5000 km.**But this is not true in the case as all bikes will be starting from the same point. And we need to find how far we can we go from that point.

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**SOLUTION 2 :**

Just launch all 50 bikes altogether from some starting point and go the distance of only

**100 km**with tanks of all bikes empty in the end.

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**SOLUTION 3 :**

1. Take all 50 bikes to 50 km so that tank of each is at

**half**.

2. Pour fuels of

**25 bikes**(half filled) into other

**25 bikes**so that their tanks are full.

3. Now, move these 25 bikes to another 50 km so that again th…

### So – who stole the apple?

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During lunch, 5 of Mr. Bryant’s students visit the supermarket.

One of the 5, stole an apple.

When questioned…

When the shop owner asked Mr. Bryant, he said that three of the boys are always truthful, but two lie all the time.

So – who stole the apple?

One of the 5, stole an apple.

When questioned…

**Jim said:**it was Hank or Tom.**Hank said:**neither Eddie or I did it.**Tom Said:**you’re both lying**Don said:**no one of them is lying, the other is speaking the truth.**Eddie said:**no Don, that’s not true.When the shop owner asked Mr. Bryant, he said that three of the boys are always truthful, but two lie all the time.

So – who stole the apple?

**And the name of the person who stole the apple is......!**### Tom is an Apple Thief!

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**What's the story behind the title?**

Let's recall who said what.

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**Jim said:**it was Hank or Tom.

**Hank said:**neither Eddie or I did it.

**Tom Said:**you’re both lying

**Don said:**no one of them is lying, the other is speaking the truth.

**Eddie said:**no Don, that’s not true.

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Clearly, Don and Eddie are making contradicting statements. Hence, one of them must be liar.

So there must be 1 more liar among Jim, Hank and Tom (since there are 2 liars & 3 truth tellers).

Tom's statement - you're both lying points Jim and Hank as liars. But there are total 2 liars with one being from either or Eddie as deduced above.

Hence,

**Tom**himself must be that other liar.

Now we are sure that Jim and Hank must be telling the truth & as told by Hank, Eddie or Hank himself is not thief.

Since, Hank is not the one who stole the app…

### Divide 1 Cube into 20 Cubes!

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From a 1987 Hungarian math contest for 11-year-olds:

How can a

How can a

**3 × 3 × 3**cube be divided into**20**cubes (not necessarily the same size)?**Cut this way to get 20 cubes....**### Division of 1 Cube into 20 cubes

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**What was the challenge?**

Mark cube for cutting 3 x 3 x 3 = 27 cubes. Cut any section of 2x2x2 = 8 cubes & cut rest of 27-8 = 19 cubes. So these 19 cubes plus 1 cube of 2x2x2 give us total number of 20 cubes.

### Need of Speed For Average Speed

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A man drives

**1 mile**to the top of a hill at**15 mph**. How fast must he drive**1 mile**down the other side to average**30 mph**for the 2-mile trip?**Here is calculation of that speed needed!**### Impossible Average Speed Challenge

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**What was average speed challenge?**

A man drives 1 mile to the top of a hill at 15 mph. That means he took, 1/15 hours i.e

**.4 minutes**to reach at the top of a hill.

To achieve average speed of

**30**mph, the man has to complete 2 miles trip in 1/15 hours i.e.

**4 minutes.**But he has

**already**taken 4 minutes to reach at the top of a hill, hence he can't achieve average speed of 30 mph over entire trip.

**MATHEMATICAL PROOF:**

Let

**'x**

**'**be the speed needed in the journey down the hill

**.**

**Average Speed = Total Distance/Total time**

**Average Speed = (1 + 1)/(1/15 + 1/x)**

30 = 2/(1/15 + 1/x)

### A Visit To Grandmother's Home!

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A father wants to take his

Can the three of them reach grandmother’s house in 3 hours?

**two**sons to visit their grandmother, who lives**33 kilometers**away. His motorcycle will cover**25 kilometers per hour**if he rides alone, but the speed drops to**20 kph**if he carries one passenger, and he cannot carry two. Each brother walks at**5 kph**.Can the three of them reach grandmother’s house in 3 hours?

**Do you think it's impossible? Click here!**### Planning Journey Towards Grandmother's Home

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**What was the challenge in the journey?**

**Yes,**all three can reach at grandmother's home within 3 hours. Here is how.

Let

**M**be the speed of motorcycle when father is alone,

**D**be the speed of motorcycle when father is with son and

**S**is speed of sons. Let

**A**and

**B**are name of the sons.

As per data, M = 25 kph, D = 20 kph, S = 5 kph.

1. Father leaves with his first son A while asking second son B to walk. Father and A drives for

**24 km**in 24/20 =

**6/5**hours. Meanwhile, son B walks (6/5) x 5 =

**6**km.

2. Now father leaves down son A for walking and drives back to son B. The distance between them is 24 -6 =

**18 km.**

3. To get back to son B, father needs

**18/(M+S)**= 18/(25+5) = 18/30 =

**3/5**hours & in that time son B walks for another (3/5) x 5 =

**3 km**

**.**Now, son B is 6 + 3 =

**9**

**km**away from source where he meets his father. While son A walks another (3/5) x 5 =

**3 km**towards grandmother's home.

4. Right now father and B are

**24 km**while A is

**6 k**

**m**away from grandmother's home. So in another 24/20 …

### Escape Safely to The Ground!

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You find yourself

You look down the four walls; they are all completely smooth and featureless,

How do you get to the bottom?

**trapped**at top an**800 foot**tall building. The surrounding land is completely flat, plus there are no other structures nearby. You need to get to the bottom, uninjured, and can only safely fall about**5**feet.You look down the four walls; they are all completely smooth and featureless,

*except*that one of the walls has a small**ledge****400****feet**above the ground. Furthermore, there are**two**hooks, one on this ledge, and one directly above it on the edge of the roof. The only tools you have are**600**feet of rope, and a knife.How do you get to the bottom?

**This should be your strategy!**### Strategy To Land Safely On The Ground

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**Why strategy needed to be planned?**

1.Tie one end of the rope to the to hook and climb down to the ledge.

2.

**Cut**(without dropping) the rope that hangs below the ledge, then

**climb back**to the roof carrying the extra rope that you cut. You now have two lengths of rope: one that is

**400 feet**long and one that is

**200 feet**long.

3.At the top, untie the rope from the hook.

Now setup the ropes like : Tie a

**small loop**at one end of the

**200-foot**long rope.

**String**the

**400-foot**long rope through the loop so that half of its length is on either side of the loop. Make sure that the loop is snug enough that the 400-foot long rope won't fall out by itself, but loose enough that you can pull the rope out later.

4. Now,

**tie**the end of the

**200**-foot rope

**without the loop**to the first hook. The 200-foot long rope lets you climb halfway to the ledge.

5.For the remaining 200 feet, you carefully climb down the

**400**-foot rope, which hangs down 200 feet from where it is held by the loop.

6.Once you …

### The Lightning Fast Addition!

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A story tells that, as a 10-year-old schoolboy, Carl Friedrich Gauss was asked to find the

How did Gauss find it?

**sum**of the**first 100**integers. The tyrannical schoolmaster, who had intended this task to occupy the boy for some time, was astonished when Gauss presented the correct answer,**5050**, almost immediately.How did Gauss find it?

**Actually, he used this trick!**### Trick for The Lightneing Fast Addition!

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**Why lightning fast speed needed?**

Gauss attached

**0**to the series and made

**pairs**of numbers having addition 100.

**100 + 0 = 100**

99 + 1 = 100

98 + 2 = 100

97 + 3 = 100

96 + 4 = 100

95 + 5 = 100

..

..

..

..

..

..

**51 + 49 = 100**

This way he got

**50 pair**of integers (ranging in between 1-100) having sum equal to

**100**.

So sum of these 50 pairs =

**100x50 = 5000.**

And the number

**50**left added to above total to get sum of integers 1 - 100 as 5000 + 50 =

**5050**

### Story of 7 Generous Dwarfs

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The

How much milk does each cup contain, if there were

**Seven**Dwarfs are having breakfast, and Snow White has just poured them some milk. Before drinking, the dwarfs have a ritual. First, Dwarf #1 splits his milk**equally**among his brothers' mugs (leaving himself with nothing). Then Dwarf #2 does the same with his milk, etc. The process continues around the table, until Dwarf #7 has distributed his milk in this way. (Note that Dwarf #7 is named Dopey!) At the end, each dwarf has**exactly**the**same**amount of milk as he started with!How much milk does each cup contain, if there were

**42**ounces of milk altogether?**Finding difficult? Click here for answer!**### Behind the Story of 7 Generous Dwarfs

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**What was the story?**

First thing is very clear that

**Dwarf 7**must have

**0**ounces of milk at the

**start**and

**end**. Let's assume that

**'a'**be the maximum amount of milk (in ounces) that any dwarf has in his mug at any point of time.

For a moment, let's assume

**Dwarf 1**himself has this

**'a'**amount of milk.

Now, when

**D1**distributes his

**'a'**amount of milk among 6 others, D7 receives

**'a/6**' amount of milk. At this point of time somebody else will be having maximum amount of milk

**'a'**. Let

**D2**be that person now having milk

**'a'**.

Next is

**D2**'s turn where he gives

**a/6**to all. So now

**D1**has

**a/6**,

**D7**has

**2a/6**and somebody else say

**D3**has maximum

**a**. Continuing in this way, for each Dwarf's turn gives -

Now, when we assumed

**D2**has

**ma**

**ximum**milk amount

**a**after receiving

**a/6**from

**D**

**1**, then it's clear that he must had earlier

**5a/6**. Similarly, D3 had maximum amount of milk

**a**after receiving

**a/6**from

**D1**and

**D2**indicates that he had

**4a/6**milk initially. Co…